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The wavelet defined by Morlet is [16]:
![$\displaystyle \hat{g}(\omega) = e^{ -2 \pi^2(\nu - \nu_0)^2}$](img594.gif) |
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(14.7) |
it is a complex wavelet which can be decomposed in two parts, one for
the real part, and the other for the imaginary part.
where
is a constant.
The admissibility condition is verified only if
.
Figure 14.1 shows these two functions.
Figure 14.1:
Morlet's wavelet: real part at left and imaginary part at right.
![\begin{figure}
\centerline{
\hbox{\psfig{figure=fig_morlet.ps,bbllx=1cm,bblly=13.5cm,bburx=20.5cm,bbury=27cm,height=5cm,width=15cm,clip=}
}}
\end{figure}](img598.gif) |
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1999-06-15